Difference between revisions of "Lmd eta three pion hlu"
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</tr> | </tr> | ||
</table> | </table> | ||
+ | ===Production channels=== | ||
+ | <table> | ||
+ | <tr> | ||
+ | <td>[[File:File:Mm2vsmmppipi.png|thrumb|left|300px|Missing mass square vs. missing mass of p&pi;+π-]]</td> | ||
+ | <td>[[File:Mm ppippim.png|thrumb|left|300px|Fit η in spectrum of missing mass of p&pi;+π- and yield 6349]]</td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | ===With or Without photon=== | ||
+ | <table> | ||
+ | <tr> | ||
+ | <td>[[File:Mpvsmmpppipi.png|thrumb|left|300px|Missing momentum vs. missing mass of p&pi;+π- after selecting missing mass around zero]]</td> | ||
+ | <td>[[File:Im pippim.png|thrumb|left|300px|Invariant mass of π+π- after requiring missing momentum smaller than 50 MeV]]</td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | ===Upper Limit=== | ||
+ | <table> | ||
+ | <tr> | ||
+ | <td>[[File:Fit im pippim.png|thrumb|left|300px|Fit of invariant mass of π+π- around η and yield upper limit of 1.64 with statistical uncertainty of bin at 5.12 and fitted yield -12.5]]</td> | ||
+ | </tr> | ||
+ | </table> | ||
+ | |||
+ | Therefore, the upper limit is 1.64/6349*0.28(fraction of all charged mode)=7.0e-5 | ||
==reference== | ==reference== | ||
[http://fr.arxiv.org/pdf/hep-ex/0411030v2 upper limit of eta with KLOE detector] | [http://fr.arxiv.org/pdf/hep-ex/0411030v2 upper limit of eta with KLOE detector] |
Revision as of 16:51, 30 October 2015
old
Statistics
Fit missing mass of proton
More
File:Eta and eta prime two pion.pdf
Form of side-band subtraction histograms
Question: Suppose there is an original function (e.g. Gaussian), what is the form of the function after bin-by-bin side-band subtraction
Answer: Suppose the function is y=f(x). The side-band subtraction makes a new function:
Test of the formula
10M events of Gaussian distribution were generated for a histograms:
side-band subtracted and plot together with the function:
source code:
test(){ const float NEvent=1e7; const int NBin=50; const float Low=-5; const float High=5; const float BinWidth=(High-Low)/NBin; TH1D* h1=new TH1D("test","test",NBin,Low,High); h1->FillRandom("gaus",NEvent); TH1D* h2=h1->Clone("subtracted"); for(int i=2;i<100;i++){ float middle=h1->GetBinContent(i); float left=h1->GetBinContent(i-1); float right=h1->GetBinContent(i+1); float result=middle-(left+right)/2.0; float error=sqrt(middle+left/2.0+right/2.0); h2->SetBinContent(i,result); h2->SetBinError(i,error); } TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))"); func->FixParameter(2,1); func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth); func->FixParameter(1,0); func->FixParameter(3,BinWidth); h2->Fit("fit"); TCanvas* c1=new TCanvas("c1","c1",696,474); h2->Draw(); TCanvas* c2=new TCanvas("c2","c2",696,474); h1->Fit("gaus"); h1->Draw(); }
Test with larg bin width
test(){ const float NEvent=1e3; const int NBin=5; const float Low=-5; const float High=5; const float BinWidth=(High-Low)/NBin; TRandom3 random(0); TH1D* h1=new TH1D("test","test",NBin,Low,High); h1->FillRandom("gaus",NEvent); TH1D* h2=h1->Clone("subtracted"); for(int i=2;i<100;i++){ float middle=h1->GetBinContent(i); float left=h1->GetBinContent(i-1); float right=h1->GetBinContent(i+1); float result=middle-(left+right)/2.0; float error=sqrt(middle+left/2.0+right/2.0); h2->SetBinContent(i,result); h2->SetBinError(i,error); } TF1* funcFix=new TF1("fit_fix","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*ga\ us(0)/([2]**4))"); funcFix->FixParameter(2,1); funcFix->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth); funcFix->FixParameter(1,0); funcFix->FixParameter(3,BinWidth); funcFix->SetLineColor(kRed); h2->Fit("fit_fix"); TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/(\ [2]**4))"); func->FixParameter(2,1); // func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth); func->FixParameter(1,0); func->FixParameter(3,BinWidth); func->SetLineColor(kBlue); h2->Fit("fit","+"); TCanvas* c1=new TCanvas("c1","c1",696,474); h2->Draw(); TCanvas* c2=new TCanvas("c2","c2",696,474); h1->Fit("gaus"); h1->Draw(); }
Test with background
test(){ const float NEvent=1e5; const float NSignal=1e5; const int NBin=20; const float Low=-5; const float High=5; const float BinWidth=(High-Low)/NBin; TRandom3 random(0); TH1D* h1=new TH1D("test","test",NBin,Low,High); h1->FillRandom("pol2",NEvent); h1->FillRandom("gaus",NSignal); TH1D* h2=h1->Clone("subtracted"); for(int i=2;i<100;i++){ float middle=h1->GetBinContent(i); float left=h1->GetBinContent(i-1); float right=h1->GetBinContent(i+1); float result=middle-(left+right)/2.0; float error=sqrt(middle+left/2.0+right/2.0); h2->SetBinContent(i,result); h2->SetBinError(i,error); } TF1* funcFix=new TF1("fit_fix","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))"); funcFix->FixParameter(2,1); funcFix->FixParameter(0,NSignal/sqrt(2*3.1416)/1*BinWidth); funcFix->FixParameter(1,0); funcFix->FixParameter(3,BinWidth); funcFix->SetLineColor(kRed); h2->Fit("fit_fix"); TF1* func=new TF1("fit","-[3]*[3]/2*(-gaus(0)/[2]/[2]+(x-[1])*(x-[1])*gaus(0)/([2]**4))"); func->FixParameter(2,1); // func->FixParameter(0,NEvent/sqrt(2*3.1416)/1*BinWidth); func->FixParameter(1,0); func->FixParameter(3,BinWidth); func->SetLineColor(kBlue); h2->Fit("fit","+"); TCanvas* c2=new TCanvas("c2","c2",696,474); h2->Draw(); TCanvas* c1=new TCanvas("c1","c1",696,474); TF1* signal_back=new TF1("signal_back","gaus(0)+pol2(2)"); signal_back->SetParameters(NEvent/sqrt(2*3.1416)/1*BinWidth,0.0,1.0,0.0,0.0,0.0); h1->Fit("signal_back"); h1->Draw(); }
apply on the data
bin width=1MeV yield/error:0.16384 limit:1.81985
bin width=2MeV yield/error:-1.69772 limit:0.491618
bin width=3MeV yield/error:-2.48978 limit:0.321244
Compare data and simu
eta prime
eta
Feldman-Cousin Method
Revive
channel
γ p → p π+π-π+π-
selecting p η prime production and η prime decay to π+π-η
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Error creating thumbnail: File missing |
Production channels
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With or Without photon
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Upper Limit
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Therefore, the upper limit is 1.64/6349*0.28(fraction of all charged mode)=7.0e-5